Planes can't depart until their destination airport weather is acceptable to land in at the expected arrival time, and all of their planned alternate airports are also available. When pilots file a flight plan, which they must do for every flight, that plan includes alternate airport options in case of problems such as their destination airport unexpectedly closing for any reason, including weather, crashes, tower outages, etc. Alternates are also chosen in case of in-flight emergencies such as an engine failure, passenger medical emergency, etc. If the forecasts for the alternate airports indicate one or more of those may be closed as well then the flight doesn't take off.

They also can't just choose more alternate airports after the fact because their fuel calculations and thus the amount of fuel they order loaded onto the plane typically wouldn't be enough. They order enough fuel for a certain amount of hold time at the destination, the ability to reach any of their alternates after holding, and some reserve. The reason they don't just fill the fuel tanks all the way up is because that would most likely put their weight, including pax and cargo, over the MTOW for the plane. Even if they didn't, they'd be burning more fuel just to fly that extra fuel around the sky, raising costs and increasing wear and tear on the engines.